A continuum mechanics model which incorporated the recovery effect by diffusion of atoms is presented to explain the initiation of grain-boundary wedge-type crack in high-temperature fatigue. The direction of deformation is periodically changed in fatigue, and the crack initiation depends on the deformation history of the grain boundary. A theoretical calculation based on the present model was made on the grain-boundary crack initiation in high-temperature fatigue where the deformation is path-dependent. The calculation results satisfactorily explained the experimental observations in polycrystalline metallic materials.